the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…
the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 1?
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 1$.
Step2: Find $f(-1)$ and $f(1)$ from the graph
From the graph, when $x=-1$, $f(-1)=0$; when $x = 1$, $f(1)=0$.
Step3: Calculate the average rate of change
Substitute $a=-1$, $b = 1$, $f(-1)=0$, and $f(1)=0$ into the formula: $\frac{f(1)-f(-1)}{1-(-1)}=\frac{0 - 0}{2}=0$.
Answer:
$0$